1. Work out how much drag the space shuttle will generate. Given that the drag of the shuttle during its descent is critical you can bet they are good at calculating this.
2. Work out how much extra thrust the 747 needs to maintain desired speed with the extra drag, and to take off with the extra weight.
3. You know how much extra thrust the engines generate, so easy to check if it is enough.
4. Work out the loads on the various bits of the airframe (eg where the wings attach). This is not easy but is the sort of thing you do when designing an aircraft so within the skill set of the team.
5. Go flying!
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